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Complexity of Ising spin glasses.

T Aspelmeier1, A J Bray, M A Moore

  • 1Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review Letters
|March 5, 2004
PubMed
Summary
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We calculated the complexity of Thouless-Anderson-Palmer (TAP) states, finding that higher-index saddle points have lower complexity. In the thermodynamic limit, all TAP states exhibit marginal stability.

Area of Science:

  • Statistical mechanics
  • Complex systems

Background:

  • The Thouless-Anderson-Palmer (TAP) theory describes spin glasses.
  • Understanding the complexity of states is crucial for characterizing complex systems.

Purpose of the Study:

  • To compute the complexity of Thouless-Anderson-Palmer (TAP) states.
  • To analyze the relationship between saddle point index and complexity.
  • To investigate the stability of TAP states in the thermodynamic limit.

Main Methods:

  • Calculation of complexity associated with minima and index-one saddle points of the TAP free energy.
  • Analysis of higher-index saddle points.

Main Results:

  • The complexity of TAP states was computed.

Related Experiment Videos

  • Higher-index saddles were found to have smaller complexities.
  • The two leading complexities were found to be equal, consistent with Morse theory.
  • In the thermodynamic limit, TAP states of all free energies become marginally stable.

    • Conclusions:

    • The complexity of TAP states is dependent on the index of saddle points.
    • Marginal stability of TAP states is a key feature in the thermodynamic limit.